The Györgyi-Field Model for the Belousov-Zhabotinsky Reaction

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The Belousov–Zhabotinsky (BZ) reaction in a continuous-flow stirred-tank reactor (CSTR) can exhibit chaos, contrary to the Oregonator model, which has no chaotic solutions.

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Deterministic chaos in the BZ reactor was studied in [1]. The scaled differential equations are:

,

,

,

,

where , , , and and the significance of all parameters ( for , , , , , , , , , and ) is given in [1].

Here, the bifurcation parameter is , the inverse of the reactor's residence time.

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Contributed by: Housam Binous, Brian G. Higgins, and Ahmed Bellagi (January 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The snapshots show several situations.

Snapshot 1: periodic behavior for

Snapshot 2: period-2 for

Snapshot 3: period-3 for

Snapshot 4: period-5 for

Snapshot 5: chaos for

Snapshots 6 and 7: finally back to period-2 and periodic behavior for and , respectively.

This bifurcation diagram (a remerging Feigenbaum tree) given below was obtained by the authors using a separate program that draws on the present Demonstration. A close look at this bifurcation diagram confirms the findings seen in the various snapshots given above.

References

[1] L. Györgyi and R. J. Field, "A Three-Variable Model of Deterministic Chaos in the Belousov-Zhabotinsky Reaction," Nature, 355, 1992 pp. 808–810. doi:10.1038/355808a0.

[2] A. Barnett, "Math 53: Chaos! - Fall 2011." (Jan 14, 2013) www.math.dartmouth.edu/~m53f11.



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